Question: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-9x-3y &= -5 \\ -7x-y &= 5\end{align*}$
Explanation: Begin by moving the $x$ -term in the second equation to the right side of the equation. $-y = 7x+5$ Divide both sides by $-1$ to isolate $y$ $y = {-7x - 5}$ Substitute this expression for $y$ in the first equation. $-9x-3({-7x - 5}) = -5$ $-9x + 21x + 15 = -5$ Simplify by combining terms, then solve for $x$ $12x + 15 = -5$ $12x = -20$ $x = -\dfrac{5}{3}$ Substitute $-\dfrac{5}{3}$ for $x$ back into the top equation. $-9( -\dfrac{5}{3})-3y = -5$ $15-3y = -5$ $-3y = -20$ $y = \dfrac{20}{3}$ The solution is $\enspace x = -\dfrac{5}{3}, \enspace y = \dfrac{20}{3}$.